Horizons is Season 2 of the game and includes the base game and the first part of the next year of updates (planetary landings on worlds without an atmosphere), with more to come over the coming year.
As far as hosting, I'm pretty sure Frontier are sorted with AWS:
Basically "Horizons" is an expansion, but differs from old school type expansions in that some of the content will be released throughout an entire year.
Elite Dangerous = Core game
Horizons = Expansion
And like with all old school expansions, they sell a bundle that includes the core game + expansion for new players.